Consider the Bertrand pricing game with n competing rms. The market demand is given by: 05 if oz Each rm has the same cost function 01(qi) = cqi. where qi is rm 13's output. The rms are not capacity constrained and can satisfy any demand they face. Consumers will buy only from the rm charging the lowest price. a) [2 points] Formulate this as a strategic game. b) [ 8 points] Characterize the set of all pure strategy Nash Equilibria assuming that if multiple rms charge the same price, they all split demand equally between them. c) [ 4 points ] Suppose now, if multiple rms charge the same price the the rm with the lowest index captures all demand (ie. if p; = pj and i